Turbulence modeling of the Von Kármán flow: Viscous and inertial stirrings

Abstract

The present work considers the turbulent Von Kármán flow generated by two counter-rotating smooth flat (viscous stirring) or bladed (inertial stirring) disks.Numerical predictions based on one-point statistical modeling using a low Reynolds number second-order full stress transport closure (RSM model) are compared to velocity measurements performed at CEA (Commissariatà l'Énergie Atomique, France). The main and significant novelty of this paper is the use of a drag force in the momentum equations to reproduce the effects of inertial stirring instead of modelling the blades themselves. The influences of the rotational Reynolds number, the aspect ratio of the cavity, the rotating disk speed ratio and of the presence or not of impellers are investigated to get a precise knowledge of both the dynamics and the turbulence properties in the Von Kármán configuration. In particular, we highlighted the transition between the merged and separated boundary layer regimes and the one between the Batchelor [1] and the Stewartson [2] flow structures in the smooth disk case. We determined also the transition between the one cell and the 2 two cell regimes for both viscous and inertial stirrings.

Turbulence Modeling of Torsional Couette Flows

“…The predictions of the RSM model have already been widely validated in various rotating disk configurations: turbulent Batchelor flows in a rotor-stator cavity (regime IV of [1]) with or without an imposed axial throughflow [2,3], with heat transfer effects [25], turbulent Stewartson flows in an open cavity with throughflow [2,3], and turbulent Von Kármán flow between counterrotating disks equipped or not with straight blades [26]. Nevertheless, to show the performances of the present model, the results of the RSM code are compared to both velocity measurements performed at IRPHE by a two-component laser Doppler anemometer and numerical predictions using the k-ε model of Launder and Sharma [27] for Re = 10 6 , G = 0.036, and several values of the flowrate coefficient C w .…”

“…Some discrepancies remain along the stator in the case of very strong inward throughflows because of the different prerotation levels used in the model and measured in the experiment [11]. Considering also the previous validations in various interdisk cavities [2,3,25,26], the RSM model can now be used with confidence for a parametric study of turbulent rotor-stator flows.…”

“…Extensive numerical predictions based on one-point statistical modeling using a low Reynolds number second-order full stress transport closure (RSM model) are performed mainly in the case of turbulent flows with merged boundary layers known as turbulent torsional Couette flows and belonging to regime III of Daily and Nece (1960). The RSM model has already shown its capability of predicting accurately the mean and turbulent fields in various rotating disk configurations (Poncet, 2005;Poncet et al, , 2008. For the first time, a detailed mapping of the hydrodynamic flow over a wide range of rotational Reynolds numbers (180 000 ≤ Re ≤ 10 000 000), aspect ratios of the cavity (0.02 ≤ G ≤ 0.05), and flow rate coefficients (−10000 ≤ C w ≤ 10000) is here provided in the turbulent torsional Couette flow regime.…”

Influence of Rotating Speed Ratio on the Annular Turbulent Flow between Two Rotating Cylinders

“…However, the work proposed here has the importance of treating a study that was not done before; it is the influence of the rotating speed ratio of the rotating cylinders on the distribution of the turbulence in the annular space and especially the relation between this parameter and the level of turbulence in this kind of flows. The same study has done by Poncet et al [17] but this study has done for rotating discs and not for rotating cylinders as we propose in our present study. The study of Iacovides and Toumpanakis [18], in which four models of turbulence are examined, proves that the model of transport of the tensions of Reynolds is the suitable level of closing to study such complex flows.…”

“…The axis of z corresponds to the axis of rotation. We note Γ the rotating speed ratio of the interior cylinder by the external one and we vary Γ from [17] has showed that the phenomena of unsteady problems and instability start have to appear only for one very high rotation corresponding to a Reynolds number of rotation higher than 10 6 . 5 2 10 …”